Time-fractional partial differential equations: a novel technique for analytical and numerical solutions

Abstract

We use the q-homotopy analysis Shehu transform method in this article to obtain analytical and numerical solutions to time fractional partial differential equations. We also give analytical solutions to two problems, as well as a comparison study in terms of absolute error with homotopy perturbation transform method, homotopy analysis transform method, and residual power series method to verify the suggested technique’s effectiveness and correctness. The numerical and graphical solutions achieved by the proposed method show that it is computationally accurate and may be used to obtain and investigate solutions to time fractional partial differential equations.

Keywords

• The q-homotopy analysis method
• fractional differential equation
• proportional delay
• Shehu transform
• Caputo approach